Rounding Algorithms for a Geometric Embedding of Minimum Multiway Cut

The multiway-cut problem is, given a weighted graph and k >= 2 terminal nodes, to find a minimum-weight set of edges whose removal separates all the terminals. The problem is NP-hard, and even NP-hard to approximate within 1+delta for some small delta > 0. Calinescu, Karloff, and Rabani (1998) gave an algorithm with performance guarantee 3/2-1/k, based on a geometric relaxation of the problem. In this paper, we give improved randomized rounding schemes for their relaxation, yielding a 12/11-approximation algorithm for k=3 and a 1.3438-approximation algorithm in general. Our approach hinges on the observation that the problem of designing a randomized rounding scheme for a geometric relaxation is itself a linear programming problem. The paper explores computational solutions to this problem, and gives a proof that for a general class of geometric relaxations, there are always randomized rounding schemes that match the integrality gap.Comment: Conference version in ACM Symposium on Theory of Computing (1999). To appear in Mathematics of Operations Researc

Non-abelian dynamics in first-order cosmological phase transitions

Bubble collisions in cosmological phase transitions are explored, taking the non-abelian character of the gauge fields into account. Both the QCD and electroweak phase transitions are considered. Numerical solutions of the field equations in several limits are presented.Comment: 8 pages, 2 figures. Contribution to the CosPA 2003 Cosmology and Particle Astrophysics Symposium. Typos correcte

Holographic Noncommutativity

We examine noncommutative Yang-Mills and open string theories using magnetically and electrically deformed supergravity duals. The duals are near horizon regions of Dp-brane bound state solutions which are obtained by using O(p+1,p+1) transformations of Dp-branes. The action of the T-duality group implies that the noncommutativity parameter is constant along holographic RG-flows. The moduli of the noncommutative theory, i.e., the open string metric and coupling constant, as well as the zero-force condition are shown to be invariant under the O(p+1,p+1) transformation, i.e., deformation independent. We find sufficient conditions, including zero force and constant dilaton in the ISO(3,1)-invariant D3 brane solution, for exact S-duality between noncommutative Yang-Mills and open string theories. These results are used to construct noncommutative field and string theories with N=1 supersymmetry from the T^(1,1) and Pilch-Warner solutions. The latter has a non-trivial zero-force condition due to the warping.Comment: latex, 40 pp. v2: minor changes, one ref. added. v3: corrections in eqs. 27 and 7

Manifestly supersymmetric M-theory

In this paper, the low-energy effective dynamics of M-theory, eleven-dimensional supergravity, is taken off-shell in a manifestly supersymmetric formulation. We show that a previously proposed relaxation of the superspace torsion constraints does indeed accommodate a current supermultiplet which lifts the equations of motion corresponding to the ordinary second order derivative supergravity lagrangian. Whether the auxiliary fields obtained this way can be used to construct an off-shell lagrangian is not yet known. We comment on the relation and application of this completely general formalism to higher-derivative (R^4) corrections. Some details of the calculation are saved for a later publication.Comment: 13 pages, plain tex. v2: minor changes, one ref. adde

Reset dynamics and latching in niobium superconducting nanowire single-photon detectors

We study the reset dynamics of niobium (Nb) superconducting nanowire single-photon detectors (SNSPDs) using experimental measurements and numerical simulations. The numerical simulations of the detection dynamics agree well with experimental measurements, using independently determined parameters in the simulations. We find that if the photon-induced hotspot cools too slowly, the device will latch into a dc resistive state. To avoid latching, the time for the hotspot to cool must be short compared to the inductive time constant that governs the resetting of the current in the device after hotspot formation. From simulations of the energy relaxation process, we find that the hotspot cooling time is determined primarily by the temperature-dependent electron-phonon inelastic time. Latching prevents reset and precludes subsequent photon detection. Fast resetting to the superconducting state is therefore essential, and we demonstrate experimentally how this is achieved